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Permission-detection of chaotic probing signals

P. Kostenko, V. Tarnapolova, D. Kakava
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Description: It was studied the resolution of chaotic pulsed signals with continuous and discrete time generated by a dynamic system described by a mathematical model in the form of the Mackay-Glass differential equation and its finite-difference approximation. By changing the parameter h in the Runge-Kutt scheme, one can control the smoothness of the obtained solution (signal), and, consequently, the width of its spectrum. The possibility of forming chaotic signals with a controlled width of the spectrum allows their use in location systems with high resolution. It is shown how the phase portrait of a chaotic pulse is transformed when the parameter h is varied. The problem of resolving the detection of chaotic pulses at unknown times of their delays is considered. With different values of “carrier” frequencies. When dividing two chaotic signals, the strategy of maximum likelihood is used. In the process of separating the two signals simultaneously solves the problem of their detection and evaluation of unknown delays. A case is considered when one signal is permission from another unknown interval of time. This case may occur when, for example, the first goal is expected at a known distance, and the second, at an unknown distance from it. In addition, signals partially overlap. As a criterion of resolution, the probability of detecting two pulses with unknown latencies is used a priori in their possible range. It is shown that chaotic pulses can be divided and it is highly probable to give reliable estimates of their delay, including in the event of their significant overlap. The results of the simulation showed that even with a small value of the signal to noise ratio q = 0.5, the greatest probability of detecting the signal from the unknown the delay of the relative known signal corresponded to the true value of this delay. In this paper, the authors carried out a statistical simulation of chaotic pulses and were investigated the characteristics of the correlation algorithm for their permission--detection.


Keywords: permission - detection, chaotic signals, Runge-Kutt scheme, Mackey-Glass equation, phase portrait

References

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Reference:
 Kostenko, P.Yu., Tarnopolova, V.V. and Kakava, D.O. (2019), “Rozdilennia-vyiavlennia khaotychnykh zonduvalnykh syhnaliv” [Permission-detection of chaotic probing signals], Information Processing Systems, Vol. 1(156), pp. 7-14. https://doi.org/10.30748/soi.2019.156.01.